K. R. Parthasarathy

K. R. Parthasarathy 's AcademicInfluence.com Rankings

K. R. Parthasarathy

Mathematics

#990

World Rank

#1708

Historical Rank

Probability Theory

#23

World Rank

#40

Historical Rank

Measure Theory

#692

World Rank

#939

Historical Rank

mathematics Degrees

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Mathematics

Why Is K. R. Parthasarathy Influential?

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According to Wikipedia, Kalyanapuram Rangachari Parthasarathy was an Indian statistician who was professor emeritus at the Indian Statistical Institute and a pioneer of quantum stochastic calculus. Parthasarathy was the recipient the Shanti Swarup Bhatnagar Prize for Science and Technology in Mathematical Science in 1977 and the TWAS Prize in 1996.

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K. R. Parthasarathy 's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Probability measures on metric spaces (1967) (1768)
An Introduction to Quantum Stochastic Calculus (1992) (1235)
PROBABILITY MEASURES IN A METRIC SPACE (1967) (637)
Positive Definite Kernels, Continuous Tensor Products, and Central Limit Theorems of Probability Theory (1972) (269)
Introduction to Probability and Measure (1979) (258)
Mathematical Foundation of Quantum Mechanics (2005) (130)
The strong perfect-graph conjecture is true for K1, 3-free graphs (1976) (125)
Representations of Complex Semi-Simple Lie Groups and Lie Algebras (1967) (116)
Representations of complex semisimple Lie groups and Lie algebras (1966) (91)
Probability distributions on locally compact abelian groups (1963) (86)
Positive Definite Functions and Operator Inequalities (2000) (83)
On the maximal dimension of a completely entangled subspace for finite level quantum systems (2004) (82)
Stochastic Integral Representation of Bounded Quantum Martingales in Fock Space (1986) (72)
An Entropic Uncertainty Principle for Quantum Measurements (2001) (72)
WHAT IS A GAUSSIAN STATE (2010) (69)
On the category of ergodic measures (1961) (64)
Quantum Stochastic Calculus (1995) (56)
The passage from random walk to diffusion in quantum probability (1988) (53)
The validity of the strong perfect-graph conjecture for (K4-e)-free graphs (1979) (47)
PROBABILITY MEASURES IN A METRIC GROUP (1967) (46)
EXTREMAL DECISION RULES IN QUANTUM HYPOTHESIS TESTING (1999) (46)
On the category of indecomposable distributions on topological groups (1962) (44)
Multipliers On Locally Compact Groups (1969) (44)
Cohomology of power sets with applications in quantum probability (1989) (42)
Extremal quantum states in coupled systems (2003) (38)
On the integral representation of the rate of transmission of a stationary channel (1961) (37)
Unique eccentric point graphs (1983) (36)
Projective unitary antiunitary representations of locally compact groups (1969) (33)
On the Generators of Quantum Stochastic Flows (1998) (33)
On Estimating the State of a Finite Level Quantum System (2004) (30)
Stable positive definite functions (1975) (28)
A new method for constructing factorisable representations for current groups and current algebras (1976) (26)
Factorisable representations of current groups and the Araki-Woods imbedding theorem (1972) (26)
From particle counting to Gaussian tomography (2015) (25)
Perfect product graphs (1977) (25)
Communication in the Presence of Noise (2013) (24)
Stop times in fock space stochastic calculus (1987) (23)
Markov chains as evans-hudson diffusions in fock space (1990) (22)
The Central Limit Theorem for the Rotation Group (1964) (20)
Enumeration of Graphs with given Partition (1968) (20)
Non-stabilizer quantum codes from Abelian subgroups of the error group (2002) (19)
QUANTUM ITO’S FORMULA (1989) (18)
Some general constructions of geodetic blocks (1982) (18)
Quantum stochastic calculus and quantum Gaussian processes (2014) (18)
Representation of a class of quantum martingales II (1988) (17)
On the cohomology of a hyperfinite action (1977) (17)
Infinitely divisible representations and positive definite functions on a compact group (1970) (17)
EXPONENTIALS OF INDICATOR FUNCTIONS ARE TOTAL IN THE BOSON FOCK SPACE Γ (L2[0,1]) (1998) (17)
Geodetic blocks of diameter three (1984) (16)
Enumeration of paths in digraphs (1964) (16)
UNIFICATION OF QUANTUM NOISE PROCESSES IN FOCK SPACES (1991) (15)
Symplectic dilations, Gaussian states and Gaussian channels (2014) (15)
Boson stochastic calculus (1985) (14)
A Family of Quantum Stabilizer Codes Based on the Weyl Commutation Relations over a Finite Field (2002) (14)
Comparison of completely positive maps on a C* algebra and a Lebesgue decomposition theorem (1996) (13)
Cospectral graphs and digraphs with given automorphism group (1975) (13)
Extension of Stationary Stochastic Processes (1964) (12)
Events, Observables and States (1992) (11)
A tool in establishing total variation convergence (1985) (11)
On the Imbedding of an Infinitely Divisible Distribution in a One-Parameter Convolution Semigroup (1967) (11)
Boson-fermion relations in several dimensions (1986) (10)
The Symmetry Group of Gaussian States in $${L}^{2}({\mathbb{R}}^{n})$$ (2011) (10)
Coding Theorems of Classical and Quantum Information Theory (2013) (9)
On the Estimation of the Spectrum of a Stationary Stochastic Process (1960) (9)
On extremal correlations (2002) (9)
A Probabilistic Proof of Bochner's Theorem on Positive Definite Functions (1967) (8)
Eigenvalues of matrix-valued analytic maps (1978) (8)
Exchangeable, stationary and entangled chains of Gaussian states (2015) (8)
J an 2 01 1 The Symmetry Group of Gaussian States in L 2 ( R n ) (2011) (7)
From quantum stochastic differential equations to Gisin-Percival state diffusion (2017) (7)
A continuous time version of Stinespring’s theorem on completely positive maps (1990) (7)
Lectures on Quantum Computation, Quantum Error Correcting Codes And Information Theory (2005) (7)
On a class of generalised Evans-Hudson flows related to classical Markov processes (1992) (7)
An extremal problem in geodetic graphs (1984) (7)
A generalised biane process (1990) (6)
Weak Convergence of Probability Measures (2005) (6)
QUANTUM PROBABILITY AND STRONG QUANTUM MARKOV PROCESSES (2003) (6)
On The g-centroidal Problem in Special Classes of Perfect Graphs (1998) (6)
On Consistency of the Maximum Likelihood Method in Testing Multiple Quantum Hypotheses (2001) (6)
In search of a complete invariant for graphs (1981) (6)
A common parametrization for finite mode Gaussian states, their symmetries, and associated contractions with some applications (2021) (5)
A stochastic Dyson series expansion (1983) (5)
On the reconstruction conjecture for separable graphs (1981) (5)
Square integrable martingales orthogonal to every stochastic integral (1978) (5)
A remark on the integration of Schrödinger equation using quantum Itô's formula (1984) (5)
On the equivalence of separability and extendability of quantum states (2016) (5)
METHOD OF FORMAL POWER SERIES IN QUANTUM STOCHASTIC CALCULUS (2000) (5)
Isographs and oriented isographs (1972) (5)
Graph characterising polynomials (1999) (5)
Obituary: Andrei Nikolaevich Kolmogorov (1988) (4)
F-Sets in graphs (1978) (4)
A Note on Idempotent Measures in Topological Groups (1967) (4)
On the derivation of the Schroedinger equation in a Riemannian manifold (1968) (4)
Positive definite kernels and continuous tensor products (1972) (4)
Limit theorems for uniformly infinitesimal families of positive definite kernels (1972) (4)
On the (4–3)-regular subgraph conjecture (1981) (4)
Extreme Points of the Convex set of Stochastic Maps on A C*-Algebra (1998) (3)
Rigidity of the poisson convolution (1990) (3)
Extreme points of the convex set of joint probability distributions with fixed marginals (2007) (3)
A note on nonisomorphic cospectral digraphs (1974) (3)
An Invitation to Quantum Information Theory (2009) (3)
SOME LIMIT THEOREMS IN REGRESSION THEORY (2016) (3)
On the Representation of Infinitely Divisible Distributins on Locally Compact Abelian Groups (1964) (3)
On the philosophy of Cramér-Rao-Bhattacharya Inequalities in Quantum Statistics (2009) (3)
On the exact bound of the Coulomb potential with respect to the Dirac operator (1978) (3)
Some remarks on the integration of Schrödinger equation using the quantum stochastic calculus (1985) (3)
Computation of sandwiched relative alpha-entropy of two n-mode gaussian states (2021) (2)
Realisation of a class of Markov processes through unitary evolutions in Fock space (1991) (2)
On a class of time inhomogenous nonsingular flows and Schrödinger operators (1982) (2)
Some additional remarks on fock space stochastic calculus (1986) (2)
A remark on the unitary group of a tensor product ofn finite-dimensional Hilbert spaces (2003) (2)
A note on Gaussian distributions in ℝn (2011) (2)
Quantum Markov Processes with a Christensen–Evans Generator in a Von Neumann Algebra (1999) (2)
A pedagogical note on the computation of relative entropy of two $n$-mode gaussian states (2021) (2)
Infinitely divisible distributions in SL(k,ℂ) or SL(k,ℝ) may be imbedded in diadic convolution semigroups (1979) (2)
Corrigendum to "A Tool in Establishing Total Variation Convergence" (1987) (2)
On the berge - sauer conjecture (1982) (2)
Semi-regular relations and digraphs (1972) (2)
Computation of sandwiched relative α-entropy of two n-mode Gaussian states (2022) (1)
Optimal quantum tomography with constrained measurements arising from unitary bases (2021) (1)
The mathematics of error correcting quantum codes (2001) (1)
Klauder-Bargmann Integral Representation of Gaussian Symmetries and Generating Functions of Gaussian States (2019) (1)
A survey of neoplasms in dogs. (1969) (1)
The Central Limit Theorem for Positive Definite Functions on Locally Compact Groups (1974) (1)
Optimal quantum tomography with constrained elementary measurements arising from unitary bases (2014) (1)
On the reconstruction of separable graphs from elementary contractions (1982) (1)
A probabilistic approach to the duality of locally compact abelian groups (1972) (1)
Feynman path integrals of operator‐valued maps (1982) (1)
Extremality and Entanglement of States in Coupled Quantum Systems (2006) (1)
Local measures in fock space stochastic calculus and a generalized ito-tanaka formula (1988) (1)
On the Kolmogorov--Wiener--Masani spectrum of a multi-mode weakly stationary quantum process (2016) (1)
An inducing construction of quantum codes from classical error correcting codes (2001) (1)
From CCR to Lévy processes: An excursion in quantum probability (2018) (1)
Extension of Measures (2005) (0)
From the Binary Alphabet to Quantum Computation (2011) (0)
A Functional Equation (1981) (0)
Quantum Coding Theorems (2013) (0)
Some highlights on the work in probability theory in India during 1980–2008: A report (2009) (0)
Borel multipliers on a locally compact group (1969) (0)
V S Varadarajan at the Indian Statistical Institute, Calcutta (2019) (0)
Probability on Boolean Algbras (2005) (0)
Correction : “A generalized biane process” (1991) (0)
Graph Code Numbers (2002) (0)
Partially Gaussian Stationary Stochastic Processes in Discrete Time (2012) (0)
Hilbert Space and conditional Expectation (2005) (0)
On structure enumeration theory (1971) (0)
Symplectic dilations, Gaussian states and Gaussian channels (2015) (0)
Standard groups with a right invariant measure (1969) (0)
SOME REMARKS ON RANDOM NUMBERS (1995) (0)
The Bertrand-Borel Debate and the Origins of the Neyman-Pearson Theory (2011) (0)
Asymptotic spectral stability of the Gisin-Percival state diffusion (2017) (0)
THE BOREL SUBSETS OF A METRIC SPACE (1967) (0)
Book review (1996) (0)
Factors, roots and embeddings of measures on Lie groups (2008) (0)
Twisted convolution quantum information channels, one-parameter semigroups and their generators (2022) (0)
Optimal quantum state determination by constrained elementary measurements (2014) (0)
Andrei Nikolaevich Kolmogorov 1 (2013) (0)
A unified approach to classical, bosonic and fermionic Brownian motions (2019) (0)
Quantum Error Correction (2013) (0)
Probability measures on [0,1] and [0,1] (2005) (0)
Andrei Nikolaevich Kolmogorov (1998) (0)
Extendability and complete extendability of Gaussian states (2016) (0)
From Information Theory to Quantum Mechanics (1986) (0)
The Duchet conjecture (1998) (0)
Probability Theory on the Lattice of Projections in a Hilbert Space (2005) (0)
NOTES ON THE SYMMETRIC GROUP ACTION IN A TOY FOCK SPACE (1998) (0)
An additional remark on unitary evolutions in Fock space (1991) (0)
Multipliers on lie groups (1969) (0)
Measures on Product Spaces (2005) (0)
NECESSARY AND SUFFICIENT CONDITIONS FOR CONSERVATIVENESS OF (1991) (0)
Book review (1997) (0)
A note on Gaussian distributions in ℝn (2012) (0)
Quantum stochastic calculus and quantum Gaussian processes (2015) (0)
Multipliers on some special groups (1969) (0)
Differential equations representation theory (2013) (0)
Systems with a Configuration Under a Group Action (2005) (0)
The mathematics of error correcting quantum codes (2001) (0)
Two remarks on Normality Preserving Borel Automorphisms of R^n (2011) (0)
PROBABILITY MEASURES IN A HILBERT SPACE (1967) (0)
Stationary Information Sources (2013) (0)
Imprimitivity Systems and Quantum Codes (2003) (0)
THE KOLMOGOROV CONSISTENCY THEOREM AND CONDITIONAL PROBABILITY (1967) (0)
PROBABILITY MEASURES ON C [0,1] AND D [0,1] (1967) (0)
Some New Examples of Lie Super-Algebra Representations Arising from Quantum Stochastic Calculus (1998) (0)
Some comments on quantum probability (1989) (0)
A TOOL IN ESTABLISHING TOTAL VARIATION CONVERGENCE1 (2010) (0)
On Some Markov Processes Arising from the Eyre-Hudson Super Lie Algebra Representations (1998) (0)
CONVERGENCE OF PROBABILITY MEASURES (1970) (0)
Harmonic Analysis Fourier Series and Beyond (2013) (0)
On a Problem in Random Walk (1966) (0)
The Basic Observables of a Quantum Mechanical System (2005) (0)
Entropy of Elementary Information Sources (2013) (0)
PROBABILITY MEASURES IN LOCALLY COMPACT ABELIAN GROUPS (1967) (0)
On the outer and inner invariants of Connes (1980) (0)
Two remarks on normality preserving Borel automorphisms of $\boldsymbol{\mathbb{R}{\kern-8.3pt}\mathbb{R}}^{{\bf \textit{n}}}$ (2013) (0)
APR Volume 20 Issue 4 Cover and Back matter (1988) (0)
Invariant Measures on Groups (2005) (0)
Stochastic Integration and Quantum Ito’s Formula (1992) (0)
The analysis of cocycles of first order on some special groups (1972) (0)
Quantum error correcting codes and Weyl commutation relations (2008) (0)
The Bush matrix over a Galois field and error correcting quantum codes (2002) (0)
Mathematical Analysis. Echoes from (2003) (0)
Extremal Quantum States in Coupled Systems in Memory of Paul André Meyer (2004) (0)
Observables and States in Tensor Products of Hilbert Spaces (1992) (0)

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